invariant to

USAGE SUMMARY

'invariant to' is a correct and commonly used phrase in written English.
You can use it when describing something that does not change in response to some external factor. For example, "The laws of physics are invariant to the observer's point of view."

✓ Grammatically correct

Science

Academia

News & Media

Human-verified examples from authoritative sources

Exact Expressions

59 human-written examples

AUDIENCE: Are these also invariant to rotation?

Massachusetts Institute of Technology

Figure 4: "Local-to-global" reciprocity is invariant to the size of the group.

Nature

This clip-limit is crisp and invariant to mammogram data.

Applied Soft Computing

The modulus of EMs is invariant to geometric transformation.

Computers & Electrical Engineering

The recognition algorithm is invariant to stroke-order, -number, and -direction, as well as invariant to rotation, scaling, and translation of symbols.

University of California, Berkeley

Full cycling times are somewhat invariant to voltage and in the 70 ms range, which equates to ∼14 Hz.

Nature

And they're invariant to a lot of the changes that I talked about before.

Massachusetts Institute of Technology

But the head model would be sort of in the sense in invariant to the torso.

Massachusetts Institute of Technology

And so being invariant to these different transformations really helps facilitate how we solve this problem.

Massachusetts Institute of Technology

And if so, can you do it invariant to actor and to viewpoint?

Massachusetts Institute of Technology

And this early representation is invariant to both actor and viewpoint.

Massachusetts Institute of Technology

Expert writing Tips

Best practice

When using "invariant to", ensure that the relationship you're describing is genuinely constant. Avoid using it when there's only a slight or negligible change, as this could mislead your audience.

Common error

Avoid using "invariant to" when describing something that is merely resistant or resilient to change. "Invariant to" implies complete lack of change, whereas resistance suggests a capacity to withstand change but not necessarily eliminate it entirely.

Linguistic Context

The phrase "invariant to" functions as a prepositional phrase that modifies a noun or noun phrase, indicating that something remains unchanged or unaffected by a particular factor. Ludwig AI confirms its correct usage.

Expression frequency: Very common

Frequent in

Science

65%

Academia

25%

News & Media

5%

Less common in

Formal & Business

3%

Encyclopedias

1%

Wiki

1%

Ludwig's WRAP-UP

In summary, "invariant to" is a grammatically correct and frequently used phrase, as confirmed by Ludwig AI, to indicate that something remains unchanged despite external factors. It's most commonly found in scientific and academic writing, where precision is key. Alternatives include "unaffected by" and "independent of". Remember to use "invariant to" only when describing true invariance, not just resistance or resilience. Proper usage ensures clear and accurate communication in technical and formal contexts.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

unaffected by

This alternative emphasizes that something remains unchanged despite the presence or influence of something else.

independent of

This highlights that the subject does not rely on or is not influenced by the specified factor.

insensitive to

This suggests a lack of reaction or change in response to a particular stimulus or condition.

resistant to

This implies that the subject can withstand or avoid being altered by something.

not susceptible to

This conveys that the subject is unlikely to be affected or changed by something.

immune to

This suggests complete protection from being changed or influenced by something.

constant under

This emphasizes that something remains the same even when certain conditions or transformations occur.

unresponsive to

This implies that there is no reaction or change in behavior in response to a stimulus.

stable with respect to

This highlights that the subject maintains its state or characteristics despite changes in a specific factor.

unvarying under

This suggests that something remains the same even when certain conditions or transformations occur.

FAQs

How can I use "invariant to" in a sentence?

You can use "invariant to" to describe something that remains unchanged despite variations in its environment or conditions. For example, "The algorithm is "invariant to" changes in lighting".

What are some alternatives to saying "invariant to"?

Alternatives include "unaffected by", "independent of", or "insensitive to", depending on the specific context. All of them maintain the idea of not suffering alterations.

Is it correct to say something is "invariant of" something else?

While "invariant" can sometimes be used with "of", the more common and grammatically preferred construction is ""invariant to"". Using "of" might sound awkward or less precise.

What does it mean for a mathematical property to be "invariant to" a transformation?

In mathematics, if a property is ""invariant to"" a transformation, it means that the property remains the same even after the transformation is applied. For example, the area of a shape is invariant to translation or rotation.